自旋为1的双层平方晶格阻挫模型的相变

卿煜林; 彭小莉; 胡爱元

doi:10.7498/aps.71.20211685

摘要

采用双时格林函数方法研究了自旋为1的双层平方晶格阻挫模型的相变行为. 详细探讨了层间耦合相互作用$ {J_{\text{c}}} $和单离子各向异性参数D对奈尔态(AF1)和共线态(AF2)之间相转换的影响. 结果显示: 只要参数$ {J_{\text{c}}} $和D不同时为零, 奈尔态和共线态在$ {J_2} = {J_1}/2 $(这里$ {J_1} $和$ {J_2} $分别描述的是系统自旋间最近邻和次近邻交换作用)时的相变温度相等, 两个态共存. 在低于相变点的温度范围内, AF1-AF2态之间可以发生相转换, 其相变类型为一阶相变. 当$ {J_2} \ne {J_1}/2 $时, 尽管AF1-AF2态有不同相变温度, 但它们也可以共存. 如果AF1(AF2)态的相变温度大, 在低温, AF1(AF2)态更稳定; 在高温, AF2(AF1)态更稳定; 在中间温度范围内, AF1-AF2态之间也可以发生一阶相转换.

关键词:

Abstract

In this paper, we investigate the phase transition of the spin-1 frustrated model on a square-lattice bilayer by the double-time Green’s function method. The effects of the interlayer coupling parameter $ {J_c} $ and single-ion anisotropy D on phase transformation between the Nèel state (AF1) and collinear state (AF2) are explored. Our results show that if only the parameters $ {J_c} $ and D are not equal to zero at the same time, the two states can exist and have the same critical temperature at $ {J_2} = {J_1}/2 $, which represents the nearest neighbor exchange. Under such parameters, a first-order phase transformation between these two states below the critical point can occur. For $ {J_2} \ne {J_1}/2 $, although both states may exist, their Neel temperatures differ from each other. If the Nèel point of the AF1 (AF2) state is larger, then at very low temperature, the AF1 (AF2) state is more stable. Thus, in an intermediate temperature, a first-order phase transition between these two states may also occur.

Keywords:

antiferromagnetic /
magnetic anisotropy /
general theory and models of magnetic ordering /
exchange and superexchange interactions

作者及机构信息

重庆师范大学物理与电子工程学院, 重庆　401331

通信作者: 胡爱元, huaiyuan@cqnu.edu.cn

基金项目: 国家自然科学基金(批准号: 11875010, 12175027)和重庆市自然科学基金(批准号: cstc2021jcyj-msxmX0168, cstc2019jcyj-msxmX0217, cstc2019jcyj-msxmX0251)资助的课题

Authors and contacts

College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China

Corresponding author: Hu Ai-Yuan, huaiyuan@cqnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11875010, 12175027) and the Natural Science Foundation of Chongqing, China (Grant Nos. cstc2021jcyj-msxmX0168, cstc2019jcyj-msxmX0217, cstc2019jcyj-msxmX0251)

文章全文

参考文献

[1]	Manojlović M, Pavkov M, Škrinjar M, PantićM, Kapor D, Stojanović S 2003 Phys. Rev. B 68 014435 Google Scholar
[2]	Manojlović M, Pavkov M, Škrinjar M, Pantić M, Kapor D, Stojanović S 2005 Phys. Rev. B 73 132510
[3]	Rutonjski M S, Radošević S M, Škrinjar M G, Pavkov-Hrvojević M V, Kapor D V, Pantić M R 2007 Phys. Rev. B 76 172506
[4]	Liu G B, Liu B G 2009 J. Phys. :Condens. Matter 21 195701 Google Scholar
[5]	Holt M, Sushkov O P, Stanek D, Uhrig G S 2011 Phys. Rev. B 83 144528 Google Scholar
[6]	Johnston D C, McQueeney R J, Lake B, Honecker A, Zhitomirsky M E, Nath R, Furukawa Y, Antropov V P, Yogesh Singh 2011 Phys. Rev. B 84 094445 Google Scholar
[7]	Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133 Google Scholar
[8]	Schmalfuß D, Darradi R, Richter J, Schulenburg J, Ihle D 2006 Phys. Rev. Lett. 97 157201 Google Scholar
[9]	Nunes W A, J Ricardo de Sousa, J Roberto Viana, Richter J 2010 J. Phys. :Condens. Matter 22 146004 Google Scholar
[10]	Nunes W A, Roberto Viana, Ricardo de Sousa J 2011 J. Stat. Mech. ???? 05016
[11]	Onofre R, Hamer C J, Oitmaa J 2011 J. Phys. :Condens. Matter 23 416001 Google Scholar
[12]	Zhuo F, Jie Q L 2014 Phys. Rev. B 89 054418 Google Scholar
[13]	Bishop R F, Li P H Y, Götze O, Richter J 2019 Phys. Rev. B 100 024401 Google Scholar
[14]	王怀玉 2012 凝聚态物理的格林函数理论 (北京: ) 第348页 Wang H Y 2012 Green’s Function in Condensed Matter Physics (Beijing: Alpha Science International Ltd and Science Press) p348 (in Chinese)
[15]	Callen H B 1963 Phys. Rev. 130 890 Google Scholar
[16]	Anderson F B, Callen H B 1964 Phys. Rev. 136 A1068 Google Scholar
[17]	Fröbrich P, Jensen P J, Kuntz P J 2000 Eur. Phys. J. B 13 477
[18]	Fröbrich P, Jensen P J, Kuntz P J, Ecker A 2000 Eur. Phys. J. B 18 579 Google Scholar
[19]	Fröbrich P, Kuntz P J 2006 Phys. Rep. 432 223 Google Scholar
[20]	Wang H Y, Zhai L J, Qian M 2014 J. Magn. Magn. Matter 354 309 Google Scholar

施引文献

图 1 奈尔态和共线态的磁构型. (a), (b)和(c), (d)分别对应层间耦合为反铁磁和铁磁相互作用. 实心和空心圆圈分别描述的是自旋取向相上和向下

Fig. 1. Spin configurations of the Néel and collinear states. (a), (b) and (c), (d) correspond to the interlayer coupling as antiferromagnetic and ferromagnetic interactions, respectively. The solid and empty circles represent the up-spins and down-spins, respectively.

下载: 全尺寸图片幻灯片

图 2 不同参数时的相变温度$ {T_N} $与$ {J_2} $之间的变化关系　(a)$ D = 0, {J_{\text{c}}} = 0.01, 0.2, 0.4, 0.6, 0.8, 1 $; (b)${J_{\text{c}}} = 0.5, D = 0, 0.2, $$ 0.4, 0.6, 0.8, 1$; (c)$ {J_{\text{c}}} = 0.5, D = 0.4 $; (d) $ D = 0, {J_{\text{c}}} = - 0.01, - 0.2, $$ - 0.4, - 0.6, - 0.8, - 1 $; (e)$ {J_{\text{c}}} = - 0.5, D = 0, 0.2, 0.4, 0.6, 0.8, 1 $; (f)$ {J_{\text{c}}} = - 0.5, D = 0.4 $

Fig. 2. Transition temperature $ {T_N} $ as a function of $ {J_2} $ for different parameters: (a)$ D = 0, $$ {J_{\text{c}}} = 0.01, 0.2, 0.4, 0.6, 0.8, 1 $; (b)${J_{\text{c}}} = $$ 0.5, D = 0, 0.2, 0.4, 0.6, 0.8, 1$; (c)$ {J_{\text{c}}} = 0.5, D = 0.4 $; (d) $ D = 0, {J_{\text{c}}} = - 0.01, - 0.2, - 0.4, - 0.6, - 0.8, - 1 $; (e)${J_{\text{c}}} = - 0.5, D = 0, $$ 0.2, 0.4, 0.6, 0.8, 1$; (f)$ {J_{\text{c}}} = - 0.5, D = 0.4 $.

下载: 全尺寸图片幻灯片

图 3 当$ D = 0.01 $时, $ {J_{\text{c}}} \geqslant 0 $的自由能F与温度T之间的变化关系

Fig. 3. Free energy F as a function of temperature T for $ {J_{\text{c}}} \geqslant 0 $ when $ D = 0.01 $.

下载: 全尺寸图片幻灯片

图 4 当$ D = 0.2 $时, 不同$ {J_{\text{c}}} $值时的自由能F与温度T之间的变化关系　(a)$ {J_{\text{c}}} = 0 $; (b)$ {J_{\text{c}}} = 0.1 $; (c)$ {J_{\text{c}}} = 0.17 $; (d) $ {J_{\text{c}}} = 0.3 $; (e)$ {J_{\text{c}}} = 0.42 $; (f)$ {J_{\text{c}}} = 1 $

Fig. 4. Free energy F as a function of temperature T for different $ {J_{\text{c}}} $ values when $ D = 0.2 $: (a) $ {J_{\text{c}}} = 0 $; (b)$ {J_{\text{c}}} = 0.1 $; (c)$ {J_{\text{c}}} = 0.17 $; (d) $ {J_{\text{c}}} = 0.3 $; (e)$ {J_{\text{c}}} = 0.42 $; (f)$ {J_{\text{c}}} = 1 $.

下载: 全尺寸图片幻灯片

图 5 当$ {J_2} = 0.5 $时, 两个态的自由能在参数${J_{\text{c}}} \text- D$空间中大小比较

Fig. 5. Comparison of the free energies of the two states in the $ {J_{\text{c}}} $ and D parameter space when $ {J_2} = 0.5 $.

下载: 全尺寸图片幻灯片

图 6 当$ {J_{\text{c}}} = 0.5, D = 0.4 $, 不同$ {J_2} $值时的自由能与温度之间的变化关系　(a) $ {J_2} = 0.4667 $; (b)$ {J_2} = 0.4675 $; (c)$ {J_2} = 0.48 $; (d) ${J_2} = $$ 0.4970.497$; (e)$ {J_2} = 0.5155 $; (f)$ {J_2} = 0.5333 $

Fig. 6. Free energy as a function of temperature for different $ {J_2} $ values when $ {J_{\text{c}}} = 0.5 $ and $ D = 0.4 $: (a) $ {J_2} = 0.4667 $; (b)${J_2} = $$ 0.4675$; (c)$ {J_2} = 0.48 $; (d) $ {J_2} = 0.497 $; (e)$ {J_2} = 0.5155 $; (f)$ {J_2} = 0.5333 $.

下载: 全尺寸图片幻灯片

图 7 当$ {J_{\text{c}}} = - 0.5, D = 0.4 $时, 不同$ {J_2} $值时的自由能与温度之间的变化关系　(a) $ {J_2} = 0.4667 $; (b)$ {J_2} = 0.467 $; (c)$ {J_2} = 0.48 $; (d) $ {J_2} = 0.4975 $; (e)$ {J_2} = 0.5156 $; (f)$ {J_2} = 0.5333 $

Fig. 7. Free energy as a function of temperature for different $ {J_2} $ values when $ {J_{\text{c}}} = - 0.5 $ and $ D = 0.4 $: (a) $ {J_2} = 0.4667 $; (b)${J_2} = $$ 0.467$; (c)$ {J_2} = 0.48 $; (d) $ {J_2} = 0.4975 $; (e)$ {J_2} = 0.5156 $; (f)$ {J_2} = 0.5333 $.

下载: 全尺寸图片幻灯片

[1]	Manojlović M, Pavkov M, Škrinjar M, PantićM, Kapor D, Stojanović S 2003 Phys. Rev. B 68 014435 Google Scholar
[2]	Manojlović M, Pavkov M, Škrinjar M, Pantić M, Kapor D, Stojanović S 2005 Phys. Rev. B 73 132510
[3]	Rutonjski M S, Radošević S M, Škrinjar M G, Pavkov-Hrvojević M V, Kapor D V, Pantić M R 2007 Phys. Rev. B 76 172506
[4]	Liu G B, Liu B G 2009 J. Phys. :Condens. Matter 21 195701 Google Scholar
[5]	Holt M, Sushkov O P, Stanek D, Uhrig G S 2011 Phys. Rev. B 83 144528 Google Scholar
[6]	Johnston D C, McQueeney R J, Lake B, Honecker A, Zhitomirsky M E, Nath R, Furukawa Y, Antropov V P, Yogesh Singh 2011 Phys. Rev. B 84 094445 Google Scholar
[7]	Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133 Google Scholar
[8]	Schmalfuß D, Darradi R, Richter J, Schulenburg J, Ihle D 2006 Phys. Rev. Lett. 97 157201 Google Scholar
[9]	Nunes W A, J Ricardo de Sousa, J Roberto Viana, Richter J 2010 J. Phys. :Condens. Matter 22 146004 Google Scholar
[10]	Nunes W A, Roberto Viana, Ricardo de Sousa J 2011 J. Stat. Mech. ???? 05016
[11]	Onofre R, Hamer C J, Oitmaa J 2011 J. Phys. :Condens. Matter 23 416001 Google Scholar
[12]	Zhuo F, Jie Q L 2014 Phys. Rev. B 89 054418 Google Scholar
[13]	Bishop R F, Li P H Y, Götze O, Richter J 2019 Phys. Rev. B 100 024401 Google Scholar
[14]	王怀玉 2012 凝聚态物理的格林函数理论 (北京: ) 第348页 Wang H Y 2012 Green’s Function in Condensed Matter Physics (Beijing: Alpha Science International Ltd and Science Press) p348 (in Chinese)
[15]	Callen H B 1963 Phys. Rev. 130 890 Google Scholar
[16]	Anderson F B, Callen H B 1964 Phys. Rev. 136 A1068 Google Scholar
[17]	Fröbrich P, Jensen P J, Kuntz P J 2000 Eur. Phys. J. B 13 477
[18]	Fröbrich P, Jensen P J, Kuntz P J, Ecker A 2000 Eur. Phys. J. B 18 579 Google Scholar
[19]	Fröbrich P, Kuntz P J 2006 Phys. Rep. 432 223 Google Scholar
[20]	Wang H Y, Zhai L J, Qian M 2014 J. Magn. Magn. Matter 354 309 Google Scholar

[1]	陈兆亮, 卢达标, 叶旭斌, 赵浩婷, 张杰, 潘昭, 迟振华, 崔田, 沈瑶, 龙有文. 钙钛矿型CeTaN₂O的高压制备及其磁性和电学性质. 物理学报, 2024, 73(8): 080702. doi: 10.7498/aps.73.20240025
[2]	任延英, 李雅宁, 柳洪盛, 徐楠, 郭坤, 徐朝辉, 陈鑫, 高峻峰. 过渡金属元素掺杂对磁铁矿磁矩及磁各向异性的调控. 物理学报, 2024, 73(6): 066104. doi: 10.7498/aps.73.20231744
[3]	孟婧, 冯心薇, 邵倾蓉, 赵佳鹏, 谢亚丽, 何为, 詹清峰. 具有不同交换偏置方向的外延FeGa/IrMn双层膜的磁各向异性与磁化翻转. 物理学报, 2022, 71(12): 127501. doi: 10.7498/aps.71.20220166
[4]	卿煜林, 彭小莉, 文林, 胡爱元. 自旋为1/2的双层平方晶格阻挫模型的基态相变. 物理学报, 2022, 71(3): 037501. doi: 10.7498/aps.71.20211584
[5]	杨雪, 杨青慧, 张怀武, 文岐业, 白飞明, 钟智勇, 张鼎, 黄建涛. 面外取向的(BiTm)₃(GaFe)₅O₁₂磁光单晶薄膜制备及取向机理分析. 物理学报, 2021, 70(10): 107801. doi: 10.7498/aps.70.20202209
[6]	黄玉昊, 张贵涛, 王如倩, 陈乾, 王金兰. 二维双金属铁磁半导体CrMoI₆的电子结构与稳定性. 物理学报, 2021, 70(20): 207301. doi: 10.7498/aps.70.20210949
[7]	卿煜林, 彭小莉, 文林, 胡爱元. 自旋为1/2的双层平方晶格阻挫模型的基态相变研究. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211584
[8]	刘祥, 米文博. Verwey相变处Fe₃O₄的结构、磁性和电输运特性. 物理学报, 2020, 69(4): 040505. doi: 10.7498/aps.69.20191763
[9]	方雨青, 金钻明, 陈海洋, 阮舜逸, 李炬赓, 曹世勋, 彭滟, 马国宏, 朱亦鸣. 高通量制备的Sm_xPr_1–xFeO₃晶体中反铁磁自旋模式和晶体场跃迁的太赫兹光谱. 物理学报, 2020, 69(20): 209501. doi: 10.7498/aps.69.20200732
[10]	文林, 胡爱元. 双二次交换作用和各向异性对反铁磁体相变温度的影响. 物理学报, 2020, 69(10): 107501. doi: 10.7498/aps.69.20200077
[11]	姜兴东, 管兴胤, 黄娟娟, 范小龙, 薛德胜. N⁺注入修复外延Fe膜面内六重磁对称. 物理学报, 2019, 68(12): 126102. doi: 10.7498/aps.68.20190131
[12]	肖嘉星, 鲁军, 朱礼军, 赵建华. 垂直磁各向异性L10-Mn1.67Ga超薄膜分子束外延生长与磁性研究. 物理学报, 2016, 65(11): 118105. doi: 10.7498/aps.65.118105
[13]	胡妮, 刘雍, 汤五丰, 裴玲, 方鹏飞, 熊锐, 石兢. La0.4Ca0.6MnO3中Mn-位Fe和Cr掺杂对磁性质的影响. 物理学报, 2014, 63(23): 237502. doi: 10.7498/aps.63.237502
[14]	陈家洛, 狄国庆. 磁各向异性热电效应对自旋相关器件的影响. 物理学报, 2012, 61(20): 207201. doi: 10.7498/aps.61.207201
[15]	胡妮, 刘雍, 程莉, 石兢, 熊锐. La0.4Ca0.6MnO3系统中Mn位Fe和Cr掺杂效应的比较性研究. 物理学报, 2011, 60(1): 017503. doi: 10.7498/aps.60.017503
[16]	张辉, 曾德长. Tb0.3Dy0.7Fe2单晶中巨磁致伸缩的逆效应. 物理学报, 2010, 59(4): 2808-2814. doi: 10.7498/aps.59.2808
[17]	刘先锋, 韩玖荣, 江学范. 阻挫三角反铁磁AgCrO2螺旋自旋序的第一性原理研究. 物理学报, 2010, 59(9): 6487-6493. doi: 10.7498/aps.59.6487
[18]	敖琪, 张瓦利, 张熠, 吴建生. Nd-Fe-B/FeCo多层纳米复合膜的结构和磁性. 物理学报, 2007, 56(2): 1135-1140. doi: 10.7498/aps.56.1135
[19]	郭玉献, 王劼, 徐彭寿, 李红红, 蔡建旺. Co0.9Fe0.1薄膜面内元素分辨的磁各向异性. 物理学报, 2007, 56(2): 1121-1126. doi: 10.7498/aps.56.1121
[20]	李锐鹏, 王　劼, 李红红, 郭玉献, 王锋, 胡志伟. 软x射线磁性圆二色吸收谱研究铁单晶薄膜的面内磁各向异性. 物理学报, 2005, 54(8): 3851-3855. doi: 10.7498/aps.54.3851

计量

文章访问数: 4385
PDF下载量: 51
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

自旋为1的双层平方晶格阻挫模型的相变